Our understanding of Antarctica is changing at an ever faster rate. For most of the time since discovering the continent we’ve thought of the ice sheet at the end of the world as a sleeping giant, stretching herself out over long ice ages but unmoved on fluttering human time scales. So when scientists began to predict the effects of global warming in the late 1970s most thought Antarctica, imperious, would take thousands of years to respond.

But a few saw instead a profound vulnerability. US glaciologists Hughes, Weertman and Mercer were among those to predict that the parts of the ice sheet lying on bedrock below sea level might be so sensitive to ocean warming or damage to their surrounding ice shelves that they would recede, retreat, disintegrate…collapse. They warned that, if true, their hypothesis of self-sustaining ice losses – ‘Marine Ice Sheet Instability’ – would mean serious consequences for sea level rise.

Four decades later, recent studies have suggested part of the West Antarctic ice sheet is indeed unstable, triggered by warm water flowing onto the continental shelf for at least a few decades. We don’t yet know if humans have made this more likely, and until now we also haven’t had confidence in predictions of how much sea level rise could result from this region and others that could become unstable from climate change. The Intergovernmental Panel on Climate Change decided in 2013 there was insufficient evidence to make an assessment any more precise than “it would not exceed several tenths of a metre” this century.

We predict Antarctic ice sheet instability will most likely contribute 10cm sea level rise by the end of the century but is extremely unlikely to contribute more than 30 cm. So ‘several’, for us, is ‘about three’.

We’re not the first to predict the consequences of Antarctic instability. So what’s new? We are the first to use all three elements I think are essential for climate predictions: physics, observations, and statistics.

First, we need physical laws – which we calculate with computer models – to give us the bounds of plausible behaviour (such as how fast ice can flow) and to account for how the future is different from the past (such as new drivers of change, or new parts of the planet responding). Of course we can’t make perfect computer models, because our knowledge and computing power are limited, so they have simplifications.

We need observations of the real world to test these physical laws and how we calculate and simplify them in models. Finally, we need statistics to combine the information from models and observations (using, in fact, the same method as a spam filter) and predict probabilities of sea level rise: in other words, to put a number on our uncertainty about the future.

Previous studies had only one or two of these. For example, they used a computer model of Antarctica (or part of it), but didn’t test it with observations or estimate its uncertainty. Or they were based on extrapolation of past observations into the future, without using much physical theory of how things might behave differently. Some were surveys of expert opinion.

We used a computer model to simulate the Antarctic ice sheet from the recent past up to the year 2200: not just once, but 3000 times. Each version was slightly different to account for ‘known unknowns’ in the physical laws and simplifications describing how ice flows and slides, the map of the bedrock beneath the ice sheet, and when instability might be triggered in each region under the mid-high climate scenario called A1B. This gave us a range of model predictions for sea level rise: three thousand possible futures fanning out from today.

We compared the simulations of the recent past with observations from the region we think is already unstable, and gave each a score from best to worst. We used the scores to give greater weight to the model versions that were most realistic: those with the most successful simplifications of the physical laws.

Testing our model with observations means we are more confident in its predictions, and the statistics mean we can quantify how confident. Crucially, that means we could put a probability on any possible value of sea level rise from Antarctic instability. We predict there is a 1 in 20 chance it will be more than 30 cm by the end of the century, a 1 in 6 chance it will exceed 21 cm, a 50:50 chance of exceeding 12 cm, and so on.

What does this mean for sea level rise? Think of two kinds of prediction we might be interested in: the most likely and worst case outcomes. Our predictions for the first are similar to the IPCC – just a few centimetres higher – so they don’t much change their assessment that global sea level rise from all sources will likely be 42 to 80 cm by the end of the century for A1B.

But for the upper limit, the IPCC made their quite vague statement because they judged the available predictions were not solid enough evidence. Those predictions reached up to one metre from Antarctic instability alone. If correct, these would hugely increase the upper limit of total sea level rise.

It’s this wild card, pessimistic outcome – the 1 in 20 bit of bad luck – that we have predicted with more thorough methods than before. And our results are much lower. We find even half a metre is outside the bounds of physical plausibility in our model, requiring rates of ice loss that violate theoretical limits or the whole ice sheet becoming immediately unstable.

Does this mean climate sceptics should be dancing in the aisles, because our study rules out these very high contributions? Not at all. When combined with other contributions, our predictions represent a significant challenge for adapting to sea level rise.

Climate sceptics and lukewarmers like to focus on the most optimistic predictions, the best possible outcomes. So here they are, just for them: we predict there is a 1 in 20 chance Antarctic instability will contribute less than 5 cm by 2100. But it’s clear we should look at the entire range of predictions if we want to make informed decisions about climate risks.

If you’re interested in doing a PhD in uncertainty about Antarctic instability, we have a project for you. It uses one of a new generation of ice sheet models that calculates more of the physics and needs fewer simplifications.

I look forward to the next generation of studies – and scientists – improving on our predictions.